CF886D.Restoration of string

A substring of some string is called the most frequent, if the number of its occurrences is not less than number of occurrences of any other substring.

You are given a set of strings. A string (not necessarily from this set) is called good if all elements of the set are the most frequent substrings of this string. Restore the non-empty good string with minimum length. If several such strings exist, restore lexicographically minimum string. If there are no good strings, print "NO" (without quotes).

A substring of a string is a contiguous subsequence of letters in the string. For example, "ab", "c", "abc" are substrings of string "abc", while "ac" is not a substring of that string.

The number of occurrences of a substring in a string is the number of starting positions in the string where the substring occurs. These occurrences could overlap.

String a is lexicographically smaller than string b, if a is a prefix of b, or a has a smaller letter at the first position where a and b differ.

某个字符串的子串被称为最频繁子串，当且仅当它的出现次数不小于该字符串中任意其他子串的出现次数。

给定一个字符串集合。一个字符串（不一定属于该集合）被称为好字符串，当且仅当该集合中的每个字符串都是这个字符串的最频繁子串。请构造一个非空的好字符串，使其长度最小；若存在多个满足条件的字符串，则选择其中字典序最小者。若不存在好字符串，则输出 "NO"（不带引号）。

字符串的一个子串是指该字符串中连续的一段字符序列。例如，"ab"、"c"、"abc" 都是字符串 "abc" 的子串，而 "ac" 不是 "abc" 的子串。

一个子串在字符串中的出现次数，是指该子串在字符串中作为连续子序列出现的起始位置的个数（允许重叠）。

字符串 $a$ 字典序小于字符串 $b$，当且仅当：$a$ 是 $b$ 的前缀，或者在 $a$ 与 $b$ 第一个不同的位置上，$a$ 在该位置的字符比 $b$ 对应位置的字符小。

The first line contains integer n (1 ≤ n ≤ 105) — the number of strings in the set.

Each of the next n lines contains a non-empty string consisting of lowercase English letters. It is guaranteed that the strings are distinct.

The total length of the strings doesn't exceed 105.

第一行包含一个整数 $n$（$1 \leq n \leq 10^5$）—— 表示集合中字符串的个数。

接下来的 $n$ 行，每行包含一个非空字符串，且仅由小写英文字母组成。保证所有字符串互不相同。

所有字符串的总长度不超过 $10^5$。

Print the non-empty good string with minimum length. If several good strings exist, print lexicographically minimum among them. Print "NO" (without quotes) if there are no good strings.

输出长度最短的非空“好字符串”。如果存在多个这样的“好字符串”，则输出其中字典序最小的一个。如果不存在“好字符串”，则输出 "NO"（不带引号）。

One can show that in the first sample only two good strings with minimum length exist: "cfmailru" and "mailrucf". The first string is lexicographically minimum.

可以证明，在第一个样例中，仅存在两个长度最短的“好字符串”："cfmailru" 和 "mailrucf"。其中，第一个字符串字典序最小。